Sum of All Tangential Component given Factor of Safety in Absence of Flow Net Calculator

Formula:

\[ \Sigma T = \frac{(c' \times L') + (\Sigma N \times \tan(\frac{\phi' \times \pi}{180}))}{fs} \]

Effective Cohesion (c'):

Length of Slip Arc (L'):

Sum of all Normal Component (ΣN):

Effective Angle of Internal Friction (φ'):

Factor of Safety (fs):

Sum of all Tangential Component (ΣT): N

1. What is Sum of All Tangential Component?

Definition: This calculation determines the total tangential force component along a potential slip surface in slope stability analysis.

Purpose: It helps geotechnical engineers assess the stability of slopes and embankments when flow net analysis is not available.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Sigma T = \frac{(c' \times L') + (\Sigma N \times \tan(\frac{\phi' \times \pi}{180}))}{fs} \]

Where:

\( \Sigma T \) — Sum of all Tangential Components (N)
\( c' \) — Effective Cohesion (Pa)
\( L' \) — Length of Slip Arc (m)
\( \Sigma N \) — Sum of all Normal Components (N)
\( \phi' \) — Effective Angle of Internal Friction (°)
\( fs \) — Factor of Safety (typically 1.3-1.5)

Explanation: The formula combines the cohesive strength and frictional strength components, divided by the safety factor.

3. Importance of This Calculation

Details: Proper calculation of tangential components is crucial for accurate slope stability analysis and preventing failures.

4. Using the Calculator

Tips: Enter all required parameters. The factor of safety includes ±5% tolerance. All values must be ≥ 0 except length and safety which must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for factor of safety?
A: For slopes, typically 1.3-1.5 is used, with ±5% tolerance considered in calculations.

Q2: How do I determine effective cohesion?
A: Effective cohesion is determined through laboratory tests like triaxial or direct shear tests.

Q3: What if I don't know the slip arc length?
A: The slip arc length must be estimated through slope geometry analysis or trial circles.

Q4: Why is the angle in degrees?
A: The calculator automatically converts degrees to radians for the tangent function.

Q5: Can this be used for all soil types?
A: Yes, but parameters must be appropriate for the specific soil conditions.